Finite Group Databasebeta

← #15786362

Subgroups — #15786362

Order 3328.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718882C211yesmaximal, characteristic
2C2×#11718882C211yesmaximal, characteristic
3C2×#11718612C212yesmaximal, complemented
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
5C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
6#13113085C212yesmaximal, complemented
7#13113081C212yesmaximal, complemented
8#13113073C212yesmaximal, complemented
9#13113066C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C2×C13×#390C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2212yes—
16C22×C42×C13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C22⋊Dic13C2212yes—
20C22×C22⋊Dic13C2212yes—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2212yes—
27C22×C4×Dic13C2211yescharacteristic
28C13×#390C418yescomplemented
29#11718882—24no—
30#11718882—24no—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C4⋊C4×Dic13—24no—
39#11718612—28no—
40C4×C4⋊Dic13—24no—
41C25×C13C2312yes—
42C22×D4×C13—22no—
43C22×D4×C13—22no—
44C22×D4×C13—22no—
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13—22no—
48C22×D4×C13C2×C414yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×Dic13C2312yes—
54C23×Dic13C2311yescharacteristic
55C23×Dic13C2311yescharacteristic
56C23×Dic13C2312yes—
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2311yescharacteristic
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4C2×C414yes—
62C2×C13×C22⋊C4—24no—
63C2×C13×C22⋊C4—24no—
64C2×C13×C22⋊C4—42no—
65C2×C13×C22⋊C4—42no—
66C2×C13×C22⋊C4C2×C418yes—
67C2×C13×C22⋊C4C2×C418yes—
68C2×C42×C13—22no—
69C2×C42×C13—22no—
70C2×C42×C13C2×C414yes—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13—24no—
73C2×C22⋊Dic13—24no—
74C2×C22⋊Dic13—24no—
75C2×C22⋊Dic13—24no—
76C2×C22⋊Dic13—24no—
77C2×C22⋊Dic13—24no—
78C2×C22⋊Dic13—24no—
79C2×C22⋊Dic13—42no—
80C2×C22⋊Dic13—42no—
81C2×C22⋊Dic13—42no—
82C2×C22⋊Dic13—42no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13D414yes—
94C2×C4⋊Dic13D414yescomplemented
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—22no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—24no—
101C2×C4×Dic13—24no—
102C2×C4×Dic13—42no—
103C2×C4×Dic13D414yes—
104#88071—24no—
105#88071—22no—
106#88071—22no—
107#88071—24no—
108#88071—24no—
109#88071—42no—
110#88071—42no—
111#14022—131nomaximal, Sylow
112C24×C13—22no—
113C24×C13—22no—
114C24×C13—22no—
115C24×C13—22no—
116C24×C13—22no—
117C24×C13—22no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—22no—
121C24×C13—22no—
122C24×C13—22no—
123C24×C13—22no—
124C24×C13—22no—
125C24×C13—22no—
126C24×C13C22×C414yes—
127C24×C13C2411yescharacteristic
128C2×D4×C13—28no—
129C2×D4×C13—28no—
130C2×D4×C13—28no—
131C2×D4×C13—44no—
132C2×D4×C13—44no—
133C2×D4×C13—44no—
134C2×D4×C13—44no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13C22×C412yes—
152C22×C4×C13C22×C414yes—
153C22×C4×C13C22×C412yes—
154C22×C4×C13C22×C412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13#4112yes—
159C22×C4×C13#4112yes—
160C22×C4×C13#4112yes—
161C22×C4×C13#4112yes—
162C22×C4×C13#4112yes—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—22no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—21no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13C2×D412yes—
199C22×Dic13C2×D414yes—
200C22×Dic13C2×D412yes—
201C22×Dic13C2×D412yes—
202C22×Dic13C2×D412yes—
203C22×Dic13#4112yes—
204C22×Dic13#4112yes—
205C13×C4⋊C4—28no—
206C13×C22⋊C4—216no—
207C13×C22⋊C4—48no—
208C42×C13—28no—
209C22⋊Dic13—48no—
210C22⋊Dic13—48no—
211C22⋊Dic13—48no—
212C22⋊Dic13—48no—
213C4⋊Dic13—28no—
214C4⋊Dic13—28no—
215C4⋊Dic13—28no—
216C4⋊Dic13—44no—
217C4×Dic13—28no—
218C4×Dic13—48no—
219C4×Dic13—44no—
220C2×#390—131no—
221C2×#390—131no—
222C2×#390D1311yescharacteristic
223C2×#388—132no—
224C2×C4×C4⋊C4—131no—
225C2×C4×C4⋊C4—131no—
226#1440—132no—
227#1439—132no—
228#1437—132no—
229C4⋊#95—131no—
230C4⋊#95—131no—
231C23×C13—24no—
232C23×C13—24no—
233C23×C13—24no—
234C23×C13—24no—
235C23×C13—24no—
236C23×C13—24no—
237C23×C13—24no—
238C23×C13—42no—
239C23×C13—42no—
240C23×C13—42no—
241C23×C13—42no—
242C23×C13—42no—
243C23×C13—42no—
244C23×C13—42no—
245C23×C13—42no—
246C23×C13—42no—
247C23×C13—42no—
248C23×C13—42no—
249C23×C13—42no—
250C23×C13—42no—
251C23×C13—42no—
252C23×C13—42no—
253C23×C13—42no—
254C23×C13—42no—
255C23×C13—42no—
256C23×C13—42no—
257C23×C13—42no—
258C23×C13—42no—
259C23×C13—42no—
260C23×C13—42no—
261C23×C13—42no—
262C23×C13—42no—
263C23×C13—42no—
264C23×C13—42no—
265C23×C13—42no—
266C23×C13C23×C411yescharacteristic
267C23×C13C22×D411yescharacteristic
268C23×C13C22×D411yescharacteristic
269C23×C13C22×D411yescharacteristic
270C23×C13C2×#4111yescharacteristic
271C23×C13C2×#4111yescharacteristic
272C23×C13C2×#4111yescharacteristic
273C23×C13C2×#4111yescharacteristic
274C23×C13C2×#4111yescharacteristic
275C23×C13C2×#4111yescharacteristic
276C23×C13C2×#4111yescharacteristic
277C23×C13H(5,𝔽2)11yescharacteristic
278C23×C13H(5,𝔽2)11yescharacteristic
279C23×C13H(5,𝔽2)11yescharacteristic
280C23×C132−1+411yescharacteristic
281D4×C13—416no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—24no—
290C2×C4×C13—24no—
291C2×C4×C13—22no—
292C2×C4×C13—24no—
293C2×C4×C13—22no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13#11714yes—
303C2×C4×C13C4×D414yes—
304C2×C4×C13C4×D414yes—
305C2×C4×C13C4×D414yes—
306C2×C4×C13#12114yes—
307C2×C4×C13#12314yes—
308C2×C4×C13#12414yes—
309C2×C4×C13#12614yes—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—24no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—24no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—24no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—42no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—42no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—42no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—42no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13—42no—
351C2×Dic13#12114yes—
352C23×D4C2×D1311yescharacteristic
353C22×C4⋊C4—131no—
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C4⋊C4C2×D1311yescharacteristic
358C22×C22⋊C4—132no—
359C22×C22⋊C4—132no—
360C22×C22⋊C4—132no—
361C22×C22⋊C4—132no—
362C22×C22⋊C4C2×D1312yes—
363C22×C22⋊C4C2×D1312yes—
364C22×C42—131no—
365C22×C42—131no—
366C22×C42—132no—
367C22×C42C2×D1311yescharacteristic
368#390—264no—
369#390—264no—
370#390Dic1318yescomplemented
371#388—268no—
372C4×C4⋊C4—264no—
373C4×C4⋊C4—264no—
374C2×#95—132no—
375C2×#95—132no—
376C2×#95—131no—
377C2×#95—132no—
378C2×#95—131no—
379C2×#95—132no—
380C2×#95—132no—
381C22×C13—44no—
382C22×C13—44no—
383C22×C13—44no—
384C22×C13—44no—
385C22×C13—44no—
386C22×C13—44no—
387C22×C13—44no—
388C22×C13—82no—
389C22×C13—82no—
390C22×C13—82no—
391C22×C13—82no—
392C22×C13—82no—
393C22×C13—82no—
394C22×C13—82no—
395C22×C13—82no—
396C22×C13C2×#11711yescharacteristic
397C22×C13C2×C4×D411yescharacteristic
398C22×C13C2×C4×D411yescharacteristic
399C22×C13C2×C4×D411yescharacteristic
400C22×C13C4×#4111yescharacteristic
401C22×C13#51811yescharacteristic
402C22×C13#52011yescharacteristic
403C22×C13C2×#12111yescharacteristic
404C22×C13C2×#12111yescharacteristic
405C22×C13C2×#12311yescharacteristic
406C22×C13#52511yescharacteristic
407C22×C13C2×#12411yescharacteristic
408C22×C13C2×#12611yescharacteristic
409C22×C13#52911yescharacteristic
410C22×C13#53211yescharacteristic
411C22×C13#53511yescharacteristic
412C22×C13#53711yescharacteristic
413C22×C13#54011yescharacteristic
414C22×C13#54211yescharacteristic
415C22×C13D4211yescharacteristic
416C22×C13#54611yescharacteristic
417C22×C13#54711yescharacteristic
418C22×C13#54811yescharacteristic
419C22×C13#55011yescharacteristic
420C22×C13#55011yescharacteristic
421C22×C13#55011yescharacteristic
422C22×C13#55311yescharacteristic
423C22×C13#55311yescharacteristic
424C22×C13#55511yescharacteristic
425C22×C13#55611yescharacteristic
426C22×C13#55611yescharacteristic
427C22×C13#55911yescharacteristic
428C22×C13#55911yescharacteristic
429C22×C13#55911yescharacteristic
430C22×C13#55911yescharacteristic
431C4×C13—24no—
432C4×C13—42no—
433C4×C13—44no—
434C4×C13#38818yescomplemented
435Dic13—24no—
436Dic13—42no—
437Dic13—42no—
438Dic13—42no—
439Dic13—44no—
440Dic13—82no—
441C25C22×D1312yes—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4C2×Dic1314yes—
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4—132no—
453C23×C4—131no—
454C23×C4—132no—
455C23×C4C22×D1312yes—
456C23×C4C22×D1311yescharacteristic
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—134no—
462C2×C4⋊C4—134no—
463C2×C4⋊C4—262no—
464C2×C4⋊C4—262no—
465C2×C4⋊C4—262no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—262no—
471C2×C4⋊C4—262no—
472C2×C4⋊C4—262no—
473C2×C4⋊C4C2×Dic1314yes—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—264no—
479C2×C22⋊C4—264no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—264no—
482C2×C22⋊C4—264no—
483C2×C22⋊C4—264no—
484C2×C22⋊C4—264no—
485C2×C22⋊C4—264no—
486C2×C22⋊C4—522no—
487C2×C22⋊C4—522no—
488C2×C22⋊C4—522no—
489C2×C22⋊C4—522no—
490C2×C22⋊C4C2×Dic1318yes—
491C2×C22⋊C4C2×Dic1318yes—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—134no—
495C2×C42—262no—
496C2×C42—262no—
497C2×C42—264no—
498C2×C42—264no—
499C2×C42—262no—
500C2×C42—262no—
501C2×C42—262no—
502C2×C42—522no—
503C2×C42C2×Dic1314yes—
504#95—262no—
505#95—262no—
506#95—264no—
507#95—264no—
508#95—264no—
509#95—522no—
510#95—522no—
511C2×C13—84no—
512C2×C13C2×#38811yescharacteristic
513C2×C13C4×#12111yescharacteristic
514C2×C13#232411yescharacteristic
515C2×C13#235411yescharacteristic
516C2×C13#235711yescharacteristic
517C2×C13#236611yescharacteristic
518C2×C13#236711yescharacteristic
519C2×C13#241411yescharacteristic
520C2×C13#241611yescharacteristic
521C2×C13#244511yescharacteristic
522C2×C13#244811yescharacteristic
523C2×C13#251211yescharacteristic
524C2×C13#251311yescharacteristic
525C2×C13#254811yescharacteristic
526C2×C13#259211yescharacteristic
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24C22×Dic1314yes—
542C24C23×D1311yescharacteristic
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—132no—
567C22×C4—132no—
568C22×C4—132no—
569C22×C4—132no—
570C22×C4—132no—
571C22×C4—134no—
572C22×C4—132no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—262no—
581C22×C4—261no—
582C22×C4—262no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—262no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—262no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—262no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—262no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4#612712yes—
609C22×C4#612712yes—
610C22×C4D4×D1312yes—
611C22×C4D4×D1312yes—
612C22×C4D4×D1312yes—
613C22×C4#612912yes—
614C22×C4#612912yes—
615C22×C4#612912yes—
616C22×C4C22×Dic1312yes—
617C22×C4C22×Dic1314yes—
618C22×C4C22×Dic1312yes—
619C22×C4C22×Dic1312yes—
620C4⋊C4—28no—
621C4⋊C4—268no—
622C4⋊C4—268no—
623C4⋊C4—268no—
624C4⋊C4—524no—
625C22⋊C4—216no—
626C22⋊C4—48no—
627C22⋊C4—528no—
628C22⋊C4—528no—
629C22⋊C4—528no—
630C22⋊C4—528no—
631C42—28no—
632C42—268no—
633C42—528no—
634C42—524no—
635C13#1402211yescharacteristic, complemented, Sylow
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23C2×#612711yescharacteristic
672C23C2×#612711yescharacteristic
673C23C2×D4×D1311yescharacteristic
674C23C2×D4×D1311yescharacteristic
675C23C2×D4×D1311yescharacteristic
676C23C2×#612911yescharacteristic
677C23C2×#612911yescharacteristic
678C23C2×#612911yescharacteristic
679C23#8825111yescharacteristic
680C23#8825111yescharacteristic
681C23#41×D1311yescharacteristic
682C23#41×D1311yescharacteristic
683C23#8825611yescharacteristic
684C23#8825711yescharacteristic
685C23C23×Dic1311yescharacteristic
686D4—416no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—134no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—264no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—264no—
724C2×C4—264no—
725C2×C4—262no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—522no—
729C2×C4—521no—
730C2×C4—521no—
731C2×C4—522no—
732C2×C4—521no—
733C2×C4—521no—
734C2×C4—522no—
735C2×C4—521no—
736C2×C4—521no—
737C2×C4—522no—
738C2×C4—521no—
739C2×C4—521no—
740C2×C4—521no—
741C2×C4—521no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4—522no—
747C2×C4—522no—
748C2×C4—522no—
749C2×C4#8813314yes—
750C2×C4#8813714yes—
751C2×C4#8813814yes—
752C2×C4#8813914yes—
753C2×C4#8818014yes—
754C2×C4D4×Dic1314yes—
755C2×C4D4×Dic1314yes—
756C2×C4D4×Dic1314yes—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22C2×#8813311yescharacteristic
773C22C2×#8813711yescharacteristic
774C22C2×#8813811yescharacteristic
775C22C2×#8813911yescharacteristic
776C22#1171924711yescharacteristic
777C22#1171925611yescharacteristic
778C22#1171925811yescharacteristic
779C22#1171926311yescharacteristic
780C22#1171926311yescharacteristic
781C22#1171926411yescharacteristic
782C22#1171926411yescharacteristic
783C22#1171926811yescharacteristic
784C22#1171930111yescharacteristic
785C22#1171930511yescharacteristic
786C22#1171930811yescharacteristic
787C22D13×#12111yescharacteristic
788C22#1171931111yescharacteristic
789C22#1171931211yescharacteristic
790C22#1171931311yescharacteristic
791C22#1171932411yescharacteristic
792C22#1171937611yescharacteristic
793C22#1171938111yescharacteristic
794C22#1171938211yescharacteristic
795C22#1171938611yescharacteristic
796C22#1171941811yescharacteristic
797C22#1171942211yescharacteristic
798C22#1171942311yescharacteristic
799C22#1171942311yescharacteristic
800C22C2×#8818011yescharacteristic
801C22C2×D4×Dic1311yescharacteristic
802C22C2×D4×Dic1311yescharacteristic
803C22C2×D4×Dic1311yescharacteristic
804C22#1171950311yescharacteristic
805C22#41×Dic1311yescharacteristic
806C22#1171953211yescharacteristic
807C4—24no—
808C4—42no—
809C4—44no—
810C4—264no—
811C4—522no—
812C4—522no—
813C4—522no—
814C4—524no—
815C4—1042no—
816C4#1171861218yescomplemented
817C2—84no—
818C2C2×#1171861211yescharacteristic
819C2#121×Dic1311yescharacteristic
820C2#1311753111yescharacteristic
821C2#1311778511yescharacteristic
822C2#1311780911yescharacteristic
823C2#1311790111yescharacteristic
824C2#1311791111yescharacteristic
825C2#1311825711yescharacteristic
826C2#1311827911yescharacteristic
827C2#1311860411yescharacteristic
828C2#1311863711yescharacteristic
829C2#1311942011yescharacteristic
830C2#1311943111yescharacteristic
831C2#1311983711yescharacteristic
832C2#1312032111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#390C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#14022
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#11718612C2semidirect
4. C2×C4⋊C4×Dic13C2semidirect
5. C2×C4×C4⋊Dic13C2semidirect
6. #13113085C2semidirect
7. #13113081C2semidirect
8. #13113073C2semidirect
9. #13113066C2semidirect
10. #13113065C2semidirect
28. C13×#390C4semidirect
94. C2×C4⋊Dic13D4semidirect
370. #390Dic13semidirect
434. C4×C13#388semidirect
635. C13#14022semidirect
816. C4#11718612semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117188822
C2×#117186122
C2×C4⋊C4×Dic132
C2×C4×C4⋊Dic132
#131130852
#131130812
#131130732
#131130662
#131130652
C2×C13×#3902
#1402213